Are the two main characters in "The Notorious Jumping Frog of Calaveras County" static or dynamic?It is also titled "The Celebrated Jumping Frog of...

A static character in literary terminology is one who
undergoes no change in their inner nature relating to values, motives, understanding, or
insights etc through the course of the narrative. In contrast, a dynamic character is
one who does undergo change in their inner nature relating to the above characteristics
through the course of the narrative. When determining whether Twain’s characters are
static or dynamic, it is important to note Twain’s purpose in telling this story about
Simon Wheeler and his friend, Jim Smiley.

Twain’s purpose is to
recount a tall yarn, or folk tale, for the sake of humor and amusement: few (if any)
ever claim to have had a personal epiphany upon completion of “The Celebrated Jumping
Frog of Calaveras County.” Since Twain’s purpose is to entertain and amuse through an
almost ridiculous tale and an equally ridiculous second narrator, there is no reason for
characters that develop and have dynamic changes to their inner character (remember the
story is a frame story with two narrators: the author of the letter to Mr. Ward and the
speaker of the tall tale, Simon Wheeler).

The answer to your question
therefore is that both characters are static characters: neither are dynamically
developing; neither Simon Wheeler not the author of the letter to Mr. Ward experience
any character change. Such character change is called character development--and neither
have it--if they were to meet after the time of the narrative, each would be as we leave
them after reading the story: tomorrow, just the same as today, static. We can see this
static, unchanging quality in the text somewhat through the first
narrator:

readability="15">

Dear Sir: -- Well, I called on good-natured,
garrulous old Simon Wheeler, and inquired after your friend, Leonidas W. Smiley ... .
But, by your leave, I did not think that a continuation of the history of the
enterprising vagabond Jim Smiley would be likely to afford me much information
concerning the Rev. Leonidas W. Smiley, and so I started
away.

We can also see
unchanging, static characterization in Simon Wheeler:

readability="12">

At the door I met the sociable Wheeler
returning, and he button-holed me and recommenced:

"Well,
thish-yer Smiley had a yeller one-eyed cow that didn't have no tail, only jest a short
stump like a bannanner, and ...."